Last visit was: 19 Nov 2025, 14:49 It is currently 19 Nov 2025, 14:49
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
605-655 Level|   Algebra|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
 [25]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
 [25]
What is the value of integer q? (1) qr + qs = r + s (2) r -s 07 Mar 2016, 09:13
2
Kudos
Add Kudos
23
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

57% (00:59) correct 43% (00:50) wrong based on 563 sessions

History

Date
Time
Result
Not Attempted Yet
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
TeamGMATIFY
User avatar
Joined: 20 Aug 2015
Last visit: 31 Oct 2016
Posts: 339
Own Kudos:
1,504
 [8]
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
Expert
Expert reply
GMAT 1: 760 Q50 V44
Posts: 339
Kudos: 1,504
 [8]
What is the value of integer q? (1) qr + qs = r + s (2) r -s Updated on: 09 Mar 2016, 04:04
Originally posted by TeamGMATIFY on 09 Mar 2016, 02:46.
Last edited by TeamGMATIFY on 09 Mar 2016, 04:04, edited 1 time in total.
2
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
Bunuel
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s
Show more

Required: q = ?

Statement 1: qr + qs = r + s
Or q (r + s) = (r+s)
(q-1)(r+s) = 0 (i)
Either q = 1 or r = -s
INSUFFICIENT

Statement 2: r ≠ -s (ii)
Nothing about q.
INSUFFICIENT

Combining Statement 1 and Statement 2:
From (i), we have (q-1)(r+s) = 0 (i)
And from (ii) r ≠ -s

Hence q = 1
SUFFICIENT

Option C
General Discussion
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 15 Nov 2025
Posts: 11,238
Own Kudos:
43,706
 [1]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,238
Kudos: 43,706
 [1]
What is the value of integer q? (1) qr + qs = r + s (2) r -s 09 Mar 2016, 03:10
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
TeamGMATIFY
Bunuel
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Required: q = ?

Statement 1: qr + qs = r + s
Or q (r + s) = (r+s)
(q-1)(r+s) = 0 (i)
Either q = 1 or r = -s
INSUFFICIENT

Statement 2: r ≠ -s (ii)
Nothing about q.
INSUFFICIENT

Combining Statement 1 and Statement 2:
From (i), we have (q-1)(r+s) = 0 (i)
And from (ii) r ≠ -s

Hence q = -1
SUFFICIENT

Option C
Show more

Hi
\(q=1\) and not -1 as shown in Red coloured portion, although the same will not effect the answer
avatar
stephyw
avatar
Joined: 11 Jun 2015
Last visit: 16 Mar 2017
Posts: 7
Own Kudos:
5
 [1]
Given Kudos: 11
Posts: 7
Kudos: 5
 [1]
What is the value of integer q? (1) qr + qs = r + s (2) r -s 30 Oct 2016, 11:47
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I'm confused why the answer is not (E).

From Statement (1):
q(r+s) = r +s
Therefore q = 1 or 0

From Statement (2):
We know (r+s) ≠ 0

Statements (1) + (2) - couldn't variable q still be 1 or 0?

Edit: Annnnnd, I just realized that q cannot be 0 because it were, statement (1) would not hold true. Too quick to post.
User avatar
mtk10
User avatar
Joined: 02 Jan 2017
Last visit: 19 Mar 2018
Posts: 46
Own Kudos:
16
Given Kudos: 23
Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34
GPA: 3.41
WE:Business Development (Accounting)
Products:
My Reviews
GMAT 1: 650 Q47 V34
Posts: 46
Kudos: 16
What is the value of integer q? (1) qr + qs = r + s (2) r -s 21 Dec 2017, 09:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
TeamGMATIFY
Bunuel
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Required: q = ?

Statement 1: qr + qs = r + s
Or q (r + s) = (r+s)
(q-1)(r+s) = 0 (i)
Either q = 1 or r = -s
INSUFFICIENT

Statement 2: r ≠ -s (ii)
Nothing about q.
INSUFFICIENT

Combining Statement 1 and Statement 2:
From (i), we have (q-1)(r+s) = 0 (i)
And from (ii) r ≠ -s

Hence q = 1
SUFFICIENT

Option C
Show more



How did you get the colored step?
How did it become (q-1)
And can someone explain why can't we do this

qr + qs = r + s

q(r+s)= r +s
q=\(\frac{(r+s)}{(r+s)}\)

divide (r+s) on both sides of the equation. The answer will be q =1 Why is this step wrong here?
User avatar
niks18
User avatar
Retired Moderator
Joined: 25 Feb 2013
Last visit: 30 Jun 2021
Posts: 867
Own Kudos:
1,763
 [3]
Given Kudos: 54
Location: India
GPA: 3.82
Products:
My Reviews
Posts: 867
Kudos: 1,763
 [3]
What is the value of integer q? (1) qr + qs = r + s (2) r -s 21 Dec 2017, 10:20
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
mtk10
TeamGMATIFY
Bunuel
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Required: q = ?

Statement 1: qr + qs = r + s
Or q (r + s) = (r+s)
(q-1)(r+s) = 0 (i)
Either q = 1 or r = -s
INSUFFICIENT

Statement 2: r ≠ -s (ii)
Nothing about q.
INSUFFICIENT

Combining Statement 1 and Statement 2:
From (i), we have (q-1)(r+s) = 0 (i)
And from (ii) r ≠ -s

Hence q = 1
SUFFICIENT

Option C



How did you get the colored step?
How did it become (q-1)
And can someone explain why can't we do this

qr + qs = r + s

q(r+s)= r +s
q=\(\frac{(r+s)}{(r+s)}\)

divide (r+s) on both sides of the equation. The answer will be q =1 Why is this step wrong here?
Show more

Hi mtk10

The highlighted portion is not correct. r & s are variables whose value you don't know.

Suppose r=2 & s=-2, then

qr + qs = r + s =>2q-2q=2-2=0. Now q can be any integer, not necessarily 1

NEVER CANCEL OUT VARIABLES

so the equation will be q(r+s)=(r+s) => q(r+s)-(r+s)=0

(r+s)(q-1)=0 so Either r+s=0 or q=-1. Hence the statement is not sufficient
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,392
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,392
What is the value of integer q? (1) qr + qs = r + s (2) r -s 20 Mar 2018, 23:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s
Show more

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (q, r and s) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
qr+qs = r+s
⇔ q(r+s) = r+s
⇔ q(r+s) - (r+s) = 0
⇔ (q-1)(r+s) = 0
⇔ q-1=0 or r+s = 0
⇔ q-1=0 since r≠-s
⇔ q = 1.

Both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
q = 1, r = 1, s = 1
q = 2, r = 1, s = -1

Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
Since we don't have information about q, condition 2) is not sufficient.

Therefore, C is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
avatar
lostnumber
avatar
Joined: 28 Mar 2018
Last visit: 22 May 2018
Posts: 38
Own Kudos:
8
Given Kudos: 20
Posts: 38
Kudos: 8
What is the value of integer q? (1) qr + qs = r + s (2) r -s 05 Apr 2018, 12:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
Bunuel
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (q, r and s) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
qr+qs = r+s
⇔ q(r+s) = r+s
⇔ q(r+s) - (r+s) = 0
⇔ (q-1)(r+s) = 0
⇔ q-1=0 or r+s = 0
⇔ q-1=0 since r≠-s
⇔ q = 1.

Both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
q = 1, r = 1, s = 1
q = 2, r = 1, s = -1

Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
Since we don't have information about q, condition 2) is not sufficient.

Therefore, C is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
Show more

Quant Newbie here and I dont understand how to get to the highlighted step, can someone explain? :?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
What is the value of integer q? (1) qr + qs = r + s (2) r -s 05 Apr 2018, 13:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
lostnumber
MathRevolution
Bunuel
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (q, r and s) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
qr+qs = r+s
⇔ q(r+s) = r+s
⇔ q(r+s) - (r+s) = 0
⇔ (q-1)(r+s) = 0
⇔ q-1=0 or r+s = 0
⇔ q-1=0 since r≠-s
⇔ q = 1.

Both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
q = 1, r = 1, s = 1
q = 2, r = 1, s = -1

Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
Since we don't have information about q, condition 2) is not sufficient.

Therefore, C is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

Quant Newbie here and I dont understand how to get to the highlighted step, can someone explain? :?
Show more

It's done by factoring out r + s from q(r + s) - (r + s) = 0:

(r + s)(q - 1) = 0.

Does this makes sense?
User avatar
Ahmed9955
User avatar
Joined: 18 Feb 2019
Last visit: 02 Dec 2023
Posts: 83
Own Kudos:
24
Given Kudos: 326
Location: India
Schools: Booth '24 Fuqua '24 ISB '23 NTU NUS Ross '24 Rotman '24 Yale '24
GMAT 1: 570 Q46 V21
Schools: Booth '24 Fuqua '24 ISB '23 NTU NUS Ross '24 Rotman '24 Yale '24
GMAT 1: 570 Q46 V21
Posts: 83
Kudos: 24
What is the value of integer q? (1) qr + qs = r + s (2) r -s 11 Apr 2020, 10:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s
Show more

Hey everyone,
On solving s1 we get (q-1)(r+s)
now, two solutions are possible whether => q=1 or r=-s

But as in the question, only the value q is asked
why do we need s2 to support s1.
S2 just tells that r=-s is not a solution.

how does this affect the value of q? As the value of will remain same

Bunuel chetan2u can you help guys?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
What is the value of integer q? (1) qr + qs = r + s (2) r -s 11 Apr 2020, 10:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ahmed9955
Bunuel
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Hey everyone,
On solving s1 we get (q-1)(r+s)
now, two solutions are possible whether => q=1 or r=-s

But as in the question, only the value q is asked
why do we need s2 to support s1.
S2 just tells that r=-s is not a solution.

how does this affect the value of q? As the value of will remain same

Bunuel chetan2u can you help guys?
Show more

Yes, from (r + s)(q - 1) = 0 it follows that r = -s OR q = 1. But notice that if q = -s, then q is not necessarily 1, it can be any other number too.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,588
Own Kudos:
1,079
Posts: 38,588
Kudos: 1,079
What is the value of integer q? (1) qr + qs = r + s (2) r -s 25 May 2024, 00:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105390 posts
kingbucky
496 posts